\subsection{可达速率域内界}\label{Cha:IC:SISO:InnerBound}
根据信息论，第$ i $个传输对的可达速率$ R^{\mathrm{IC,SISO}}_i $下界为
\begin{subequations}
    \begin{align}
    R^{\mathrm{IC,SISO}}_i &=\maximize{\left\{f_i\left(x_i\right)\right\}}{I\left(X_i;Y_i\right)}\\
    &=\maximize{\left\{f_i\left(x_i\right)\right\}}{h\left(Y_i\right)-h\left(Y_i\vert X_i\right)}\\
    &=\maximize{\left\{f_i\left(x_i\right)\right\}}{h\left(\sum_{j=1}^{K}g_{i,j}\left(X_j+b_j\right)+Z_i\right)-h\left(\sum_{j=1,j\neq i}^{K}g_{i,j}\left(X_j+b_j\right)+Z_i\right)}\\
    &\geq \maximize{\left\{f_i\left(x_i\right)\right\}}{\frac{1}{2}\log_2\left(\sum_{j=1}^{K}2^{2 h\left(g_{i,j} X_j\right)}+2^{2 h\left(Z_i\right)}\right)}\nonumber\\
    &\quad\quad\quad\quad\quad\quad\quad\quad\quad-\frac{1}{2}\log_2 2\pi e \var{\sum_{j=1,j\neq i}^{K}g_{i,j}\left(X_j+b_j\right)+Z_i}\label{Eqn:IC:SISO:InnerBound:d}\\
    &=\maximize{\left\{f_i\left(x_i\right)\right\}}{\frac{1}{2}\log_2\left(\sum_{j=1}^{K}{g_{i,j}^2 2^{2 h\left( X_j\right)}}+2\pi e \sigma^2\right)}\nonumber\\
    &\quad\quad\quad\quad\quad\quad\quad\quad\quad-\frac{1}{2}\log_2{\left(2\pi e \sum_{j=1,j\neq i}^{K}g_{i,j}^2\varepsilon_j+2\pi e \sigma^2\right)},\label{Eqn:IC:SISO:InnerBound:e}
    \end{align}
\end{subequations}
式中，不等式\eqref{Eqn:IC:SISO:InnerBound:d}是根据熵功率不等式，以及对于给定方差$ \var{Q} $的任意随机变量$ Q $，有$ h\left(Q\right)\leq \frac{1}{2}\log_2{2\pi e \var{Q}} $。

由表达式\eqref{Eqn:IC:SISO:InnerBound:e}的单调性知，通过最大化微分熵$ \left\{h\left(X_j\right)\right\} $，可以获得可达速率$ R^{\mathrm{IC,SISO}}_i $的最大下界。将定理\ref{Thm:P2P:SISO:Lower:ABG}的ABG分布的微分熵\eqref{Eqn:P2P:SISO:Lower:MaxEntropy:EntropyVal}代入至\eqref{Eqn:IC:SISO:InnerBound:e}中，得
\begin{align}
R^{\mathrm{IC,SISO}}_i &\geq \frac{1}{2}\log_2{\left(\frac{2\pi\sigma^2+\sum_{j=1}^{K}g_{i,j}^2 e^{1+2\left(\alpha_j+\gamma_j\varepsilon_j\right)}}{2\pi\sigma^2+2\pi \sum_{j=1,j\neq i}^{K}g_{i,j}^2\varepsilon_j}\right)}\label{Eqn:IC:SISO:InnerBound:ABG}.
\end{align}



因此，可见光干扰信道可达速率域的内界（ABG内界）可以表示为
\begin{align}
\begin{cases}
R^{\mathrm{IC,SISO}}_1 &\leq \frac{1}{2}\log_2{\left(\frac{2\pi\sigma^2+\sum_{j=1}^{K}g_{1,j}^2e^{1+2\left(\alpha_j+\gamma_j\varepsilon_j\right)}}{2\pi\sigma^2+2\pi \sum_{j=2}^{K}g_{1,j}^2\varepsilon_j}\right)},\\
&\vdots\\
R^{\mathrm{IC,SISO}}_K &\leq\frac{1}{2}\log_2{\left(\frac{2\pi\sigma^2+\sum_{j=1}^{K}g_{K,j}^2e^{1+2\left(\alpha_j+\gamma_j\varepsilon_j\right)}}{2\pi\sigma^2+2\pi \sum_{j=1}^{K-1}g_{K,j}^2\varepsilon_j}\right)}.
\end{cases}
\end{align}